On moderate deviations for martingales
Copyright policy )On moderate deviations for martingales
Let Xn = (Xnt,Fnt)0 ≤ t ≤ 1 be the square integrable martingales with the quadratic characteristics ⟨Xn⟩, n = 1, 2, .... We have proved that the large deviation relation P(Xn1 ≥ r)/(1 - Φ(r)) → 1 is valid with r growing to infinity at some rate depending on Ln2δ = E ∑0 ≤ t ≤1 |Δ Xnt |2+2δ and Nn2δ = E|⟨Xn⟩1 -1|1+δ, where δ > 0 and Ln2δ → 0, Nn2δ → 0 as n → ∞. The exact bound for the remainder is obtained too.
Preprint: Weierstraß-Institut für Angewandte Analysis und Stochastik, vol. 121
ddc:510, [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], martingale, article, central limit theorem, Martingale -- central limit theorem -- rate of convergence -- moderate deviation, Martingales with continuous parameter, moderate deviation, Approximations to statistical distributions (nonasymptotic), 510, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Large deviations, central limit theorem -- martingale -- moderate deviation -- rate of convergence, Martingale, 62E17, 60G44, 60F10, rate of convergence
ddc:510, [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], martingale, article, central limit theorem, Martingale -- central limit theorem -- rate of convergence -- moderate deviation, Martingales with continuous parameter, moderate deviation, Approximations to statistical distributions (nonasymptotic), 510, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Large deviations, central limit theorem -- martingale -- moderate deviation -- rate of convergence, Martingale, 62E17, 60G44, 60F10, rate of convergence
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